Broadband connection?
It is normal for the icons of local connection and broadband connection to appear after broadband installation. As for the local connection is limited or disconnected, you can ignore it as long as it does not affect the Internet access, but you can try to set an IP address manually to repair it: Right click "Network Neighborhood" on the desktop/Properties/Local Area Connection/Properties/Select "Internet Protocol (TCP/IP)" in the "General" column/Properties/In